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Pol Grasland-Mongrain edited Simu disp maps.tex
over 8 years ago
Commit id: 902eef90f8cc8564df82120f9a1bad0f7bf39031
deletions | additions
diff --git a/Simu disp maps.tex b/Simu disp maps.tex
index 3ae0168..f331515 100644
--- a/Simu disp maps.tex
+++ b/Simu disp maps.tex
...
\begin{equation}
G_y = \frac{\cos \beta \sin \beta}{4\pi \rho c_p^2 r} \delta_P + \frac{-\sin \beta \cos \beta}{4\pi \rho c_s^2 r} \delta_S + \frac{3\cos \beta \sin \beta}{4\pi \rho r^3} \tau Rect\\
G_z %G_z = \frac{\cos^2 \beta}{4\pi \rho c_p^2 r} \delta_P + \frac{\sin^2 \beta}{4\pi \rho c_s^2 r} \delta_S + \frac{3\cos^2 \beta-1}{4\pi \rho r^3} \tau Rect \\
\label{eq:akirichards}
\end{equation}
where $\beta$ is the angle between the applied force and the axis y or z, $\rho$ the medium density, $c_p$ and $c_s$ the compression and shear wave speed respectively, $\delta_S$ and $\delta_P$ Dirac distribution indicating the position of the compression and shear waves along space and time, $\tau$ the time and $Rect$ the near-field term. The three terms correspond respectively to the far-field compression wave, the far-field shear wave and the near-field term.